Answer
$$\frac{30\sqrt{3}}{7\sqrt{5}}=\frac{6\sqrt{15}}{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{30\sqrt{3}}{7\sqrt{5}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{30\sqrt{3}}{7\sqrt{5}}\frac{\sqrt{5}}{\sqrt{5}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{30\sqrt{15}}{35} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 30 \sqrt{ 15 } : \color{blue}{ 5 } } { 35 : \color{blue}{ 5 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{6\sqrt{15}}{7}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{5}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 30 \sqrt{3} } \cdot \sqrt{5} = 30 \sqrt{15} $$ Simplify denominator. $$ \color{blue}{ 7 \sqrt{5} } \cdot \sqrt{5} = 35 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 5 } $. |
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